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arXiv 0807.1517hep-th
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含时耦合的规范理论及其宇宙学对偶

Gauge Theories with Time Dependent Couplings and their Cosmological Duals

Adel Awad, Sumit R. Das, Suresh Nampuri, K. Narayan, Sandip P. Trivedi

备注：
45 pages, 1 figure; v2. minor modifications; v3: PRD version, conclusions in the field theory case significantly revised to include possible renormalization effects, quantum mechanics toy model unchanged, abstract and introduction revised, additional subsection 4.1 added
发表信息：
Phys.Rev.D79:046004,2009
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摘要：

我们考虑平坦3+1维时空中的N=4 SYM理论，耦合常数随时间变化，在$t=0$处为零，如$g_{YM}^2=t^p$。在类似的量子力学玩具模型中，我们发现响应是奇异的。对于一般状态，能量在$t=0$处发散。此外，如果$p>1$波函数的相位具有剧烈振荡的行为，这不允许它继续超过$t=0$。类似的效应也会使规范理论变得奇异，尽管重整化的非平凡效应可以驯服这种奇异性，并允许在$t=0$之外的光滑延拓。在某些情况下，引力对偶是一种依赖于时间的宇宙学，它在$t=0$处表现出类空奇点。如果我们的结果适用于耦合消失的规范理论，则意味着奇点是一种真正的疾病，不允许有意义的延续。当耦合保持非零并且在$t=0$处变小时，体中的曲率变为弦尺度的量级。规范理论现在承认在这一点之外还有时间演化。在这种情况下，会产生有限的能量，这可能会热化并导致大块的黑洞。

英文摘要：

We consider the N=4 SYM theory in flat 3+1 dimensional spacetime with a time dependent coupling constant which vanishes at $t=0$, like $g_{YM}^2=t^p$. In an analogous quantum mechanics toy model we find that the response is singular. The energy diverges at $t=0$, for a generic state. In addition, if $p>1$ the phase of the wave function has a wildly oscillating behavior, which does not allow it to be continued past $t=0$. A similar effect would make the gauge theory singular as well, though nontrivial effects of renormalization could tame this singularity and allow a smooth continuation beyond $t=0$. The gravity dual in some cases is known to be a time dependent cosmology which exhibits a space-like singularity at $t=0$. Our results, if applicable in the gauge theory for the case of the vanishing coupling, imply that the singularity is a genuine sickness and does not admit a meaningful continuation. When the coupling remains non-zero and becomes small at $t=0$, the curvature in the bulk becomes of order the string scale. The gauge theory now admits a time evolution beyond this point. In this case, a finite amount of energy is produced which possibly thermalizes and leads to a black hole in the bulk.

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